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harmonic_entropy · A list dedicated to the exploration of harmonic entropy models of musical consonance
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Fwd: Re: Harmonic entropy   Message List  
Reply | Forward Message #517 of 1055 |
Open questions

How 'bout it, Gene? I've made correction

> Open questions:
>
> Is there a function, F(x,y), such that F(entropy,s) is invariant to
> changes in N? For s=1%, F(entropy,1%) = exp(entropy/2.3) seemed to
> work.

Invariant except for a constant, which it would good to be able to
calculate.

> Can we explicitly calculate what this function converges to for N-
> >infinity? Or at least prove that is does converge, and calculate
the
> limit to some computational error?

Again up to an arbitrary constant.

> Can we prove that the observations mentioned above (about the local
> minima and about proxying for the width being OK) are in some sense
> true?

This one should be the easiest (see the original message, about four
messages ago, for the observations).




Sun Dec 2, 2001 6:20 am

paulerlich
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Message #517 of 1055 |
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... Well, there are variations. But it's always a function (meant to reflect one component of dissonance) of a precise specified input interval or chord. And...
Paul Erlich
paulerlich
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Nov 18, 2001
2:20 am

... future ... rule ... p ... The ... The "actual input value" is a certain number of cents, so how can a normal curve be centered around it? The ... A "dyad"...
Paul Erlich
paulerlich
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Nov 18, 2001
2:20 am

... Right. ... If the number of cents is c, the curve is y=1/(s*sqrt(2*pi))*exp((x-c)^2/2*s^2) where x is the position on the interval axis (have you looked at...
Paul Erlich
paulerlich
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Nov 18, 2001
2:20 am

How 'bout it, Gene? I've made correction ... Invariant except for a constant, which it would good to be able to calculate. ... the ... Again up to an arbitrary...
Paul Erlich
paulerlich
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Dec 2, 2001
6:20 am
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